What is P(θ-π) if (-8,15) lies on the terminal side of θ?

Answer 1

just switch the signs (-8,15) to P(8,-15)

this is an 8-15-17 right triangle tan^-1(15/8)=tan^-1(1.85) = 61.93 degrees or .344pi radians

(-8,15) is in the 2nd where x<0 and y>0

theta = pi - .344pi = 0.656 pi in the 2nd quadrant and

theta - pi = pi -.344pi - pi = -0.344pi in the 4th quadrant with the point P(8,-15)

theta is very close to 2pi/3, and subtracting pi = -pi/3 or 5pi/6

theta is very close to 120 degrees with theta-pi = -60 or 330 degrees